The home side showed the glimpses of brilliance that allowed them to beat Deportivo La Coruna in the previous round, as Victor Curto shot from distance in the first few minutes to hit the crossbar.
Jaen found themselves going into half time 1-0 down, though, as David Lopez tucked home two minutes into first-half injury time.
However, the hosts did not give up and levelled in the 65th minute when Juanma put in an inviting cross that was headed into the net by Espanyol defender Sidnei.
The home side soon took the lead in the 70th minute when Jozabed turned in a rebound after Fran Machado had struck the bar.
It looked as though Jaen would take a vital lead into the second leg, but Christian Stuani thumped home from close range as the game edged closer to the final whistle to help earn his side a first-leg draw.